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In the natural sciences, a vector quantity (also known as a vector physical quantity, physical vector, or simply vector) is a vector-valued physical quantity. [9] [10] It is typically formulated as the product of a unit of measurement and a vector numerical value (), often a Euclidean vector with magnitude and direction.
Given a subset S of R n, a vector field is represented by a vector-valued function V: S → R n in standard Cartesian coordinates (x 1, …, x n).If each component of V is continuous, then V is a continuous vector field.
A vector pointing from A to B. In mathematics, physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector [1] or spatial vector [2]) is a geometric object that has magnitude (or length) and direction.
In Poynting's original paper and in most textbooks, the Poynting vector is defined as the cross product [4] [5] [6] =, where bold letters represent vectors and . E is the electric field vector;
In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1. A unit vector is often denoted by a lowercase letter with a circumflex, or "hat", as in ^ (pronounced "v-hat").
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A four-vector A is a vector with a "timelike" component and three "spacelike" components, and can be written in various equivalent notations: [3] = (,,,) = + + + = + = where A α is the magnitude component and E α is the basis vector component; note that both are necessary to make a vector, and that when A α is seen alone, it refers strictly to the components of the vector.
Applying the techniques of mathematical physics to classical mechanics typically involves the rigorous, abstract, and advanced reformulation of Newtonian mechanics in terms of Lagrangian mechanics and Hamiltonian mechanics (including both approaches in the presence of constraints).